Spectral Causality Research Articles

Fear Linkages Between the US and BRICS Stock Markets: A Frequency-Domain Causality

We employ a spectral causality approach to uncover short-, medium-, and long-run causal relations between the US implied volatility index and the five individual implied volatility indexes of BRICS markets from 16th March 2011 to 31st January 2018. We show that the volatility causal relations differ between the short and long run in many cases. Although the results indicate the dominant role played by US uncertainty in shaping uncertainty in all BRICS markets, there is also evidence of a feedback effect from Brazil, Russia, and China to the US that differs across the spectrum. The implications for hedging and risk management practices are explored.

Foreign direct investment and growth causal-nexus in economic community of West African States: Evidence from spectral causality

The paper examines the causal relationship between FDI and economic growth (GDP) in thirteen ECOWAS countries using both time domain and frequency domain testing procedures using annual data from 1970 to 2015. The results showed that time domain is not adequate in detecting causality. The time domain detected causality in only four out of thirteen countries whilst the frequency domain detected causality at different frequencies and cycles in nine out of thirteen countries. The findings of this study indicate the importance of frequency domain causality, that it decomposes causality at different frequencies and subsequently detects causality at certain cycles lengths. The general observation that economic growth leads FDI calls for ECOWAS leaders to rethink about painful sacrifices they make to attract FDI into the region.

Foreign direct investment and growth causal-nexus in economic community of West African States: Evidence from spectral causality

The paper examines the causal relationship between FDI and economic growth (GDP) in thirteen ECOWAS countries using both time domain and frequency domain testing procedures using annual data from 1970 to 2015. The results showed that time domain is not adequate in detecting causality. The time domain detected causality in only four out of thirteen countries whilst the frequency domain detected causality at different frequencies and cycles in nine out of thirteen countries. The findings of this study indicate the importance of frequency domain causality, that it decomposes causality at different frequencies and subsequently detects causality at certain cycles lengths. The general observation that economic growth leads FDI calls for ECOWAS leaders to rethink about painful sacrifices they make to attract FDI into the region.

Granger causality revisited

This technical paper offers a critical re-evaluation of (spectral) Granger causality measures in the analysis of biological timeseries. Using realistic (neural mass) models of coupled neuronal dynamics, we evaluate the robustness of parametric and nonparametric Granger causality. Starting from a broad class of generative (state-space) models of neuronal dynamics, we show how their Volterra kernels prescribe the second-order statistics of their response to random fluctuations; characterised in terms of cross-spectral density, cross-covariance, autoregressive coefficients and directed transfer functions. These quantities in turn specify Granger causality — providing a direct (analytic) link between the parameters of a generative model and the expected Granger causality. We use this link to show that Granger causality measures based upon autoregressive models can become unreliable when the underlying dynamics is dominated by slow (unstable) modes — as quantified by the principal Lyapunov exponent. However, nonparametric measures based on causal spectral factors are robust to dynamical instability. We then demonstrate how both parametric and nonparametric spectral causality measures can become unreliable in the presence of measurement noise. Finally, we show that this problem can be finessed by deriving spectral causality measures from Volterra kernels, estimated using dynamic causal modelling.

Assessing dynamic spectral causality by lagged adaptive directed transfer function and instantaneous effect factor.

It is of significance to assess the dynamic spectral causality among physiological signals. Several practical estimators adapted from spectral Granger causality have been exploited to track dynamic causality based on the framework of time-varying multivariate autoregressive (tvMVAR) models. The nonzero covariance of the model's residuals has been used to describe the instantaneous effect phenomenon in some causality estimators. However, for the situations with Gaussian residuals in some autoregressive models, it is challenging to distinguish the directed instantaneous causality if the sufficient prior information about the "causal ordering" is missing. Here, we propose a new algorithm to assess the time-varying causal ordering of tvMVAR model under the assumption that the signals follow the same acyclic causal ordering for all time lags and to estimate the instantaneous effect factor (IEF) value in order to track the dynamic directed instantaneous connectivity. The time-lagged adaptive directed transfer function (ADTF) is also estimated to assess the lagged causality after removing the instantaneous effect. In this study, we first investigated the performance of the causal-ordering estimation algorithm and the accuracy of IEF value. Then, we presented the results of IEF and time-lagged ADTF method by comparing with the conventional ADTF method through simulations of various propagation models. Statistical analysis results suggest that the new algorithm could accurately estimate the causal ordering and give a good estimation of the IEF values in the Gaussian residual conditions. Meanwhile, the time-lagged ADTF approach is also more accurate in estimating the time-lagged dynamic interactions in a complex nervous system after extracting the instantaneous effect. In addition to the simulation studies, we applied the proposed method to estimate the dynamic spectral causality on real visual evoked potential (VEP) data in a human subject. Its usefulness in time-variant spectral causality assessment was demonstrated through the mutual causality investigation of brain activity during the VEP experiments.

A Nonlinear Generalization of Spectral Granger Causality

Spectral measures of linear Granger causality have been widely applied to study the causal connectivity between time series data in neuroscience, biology, and economics. Traditional Granger causality measures are based on linear autoregressive with exogenous (ARX) inputs models of time series data, which cannot truly reveal nonlinear effects in the data especially in the frequency domain. In this study, it is shown that the classical Geweke's spectral causality measure can be explicitly linked with the output spectra of corresponding restricted and unrestricted time-domain models. The latter representation is then generalized to nonlinear bivariate signals and for the first time nonlinear causality analysis in the frequency domain. This is achieved by using the nonlinear ARX (NARX) modeling of signals, and decomposition of the recently defined output frequency response function which is related to the NARX model.

Trend and cyclical decoupling: new estimates based on spectral causality tests and wavelet correlations

The issue of decoupling of emerging market economies (EMEs) (especially in the Asian region) from the developments in advanced economies has become a subject of lively debate in recent years. Basically, decoupling seems to comprise three sub-hypotheses: (i) growth spillovers from advanced countries to EMEs decreasing progressively in importance, (ii) business cycles in EMEs becoming less synchronized with those of the advanced world and (iii) strengthening of growth spillovers and cyclical synchronization among the EMEs as a group. The received literature fails to distinguish adequately between the trend and cyclical aspects of the decoupling relationship. We resort to two frequency domain methods (nonstationary spectral causality testing and wavelet correlations), which seem to offer a neat separation of trend and cyclical decoupling. Based on a sample of seven EMEs from the Asian region (including the two large EMEs – China and India), we uncover strong evidence favouring both trend and cyclical decoupling.

Causality analysis of neural connectivity: New tool and limitations of spectral Granger causality

Granger causality (GC) is one of the most popular measures to reveal causality influence of time series based on the estimated linear regression model and has been widely applied in economics and neuroscience due to its simplicity, understandability and easy implementation. Especially, its counterpart in frequency domain, spectral GC, has recently received growing attention to study causal interactions of neurophysiological data in different frequency ranges. In this paper, on the one hand, for one equality in the linear regression model (frequency domain) we point out that all items at the right-hand side of the equality make contributions (thus have causal influence) to the unique item at the left-hand side of the equality, and thus a reasonable definition for causality from one variable to another variable (i.e., the unique item) should be able to describe what percentage the variable occupies among all these contributions. Along this line, we propose a new spectral causality definition. On the other hand, we point out that spectral GC has its inherent limitations because of the use of the transfer function of the linear regression model and as a result may not reveal real causality at all and lead to misinterpretation result. By one example we demonstrate that the results of spectral GC analysis are misleading but the results from our definition are much reasonable. So, our new tool may have wide potential applications in neuroscience.

Causality Analysis of Neural Connectivity: Critical Examination of Existing Methods and Advances of New Methods

Granger causality (GC) is one of the most popular measures to reveal causality influence of time series and has been widely applied in economics and neuroscience. Especially, its counterpart in frequency domain, spectral GC, as well as other Granger-like causality measures have recently been applied to study causal interactions between brain areas in different frequency ranges during cognitive and perceptual tasks. In this paper, we show that: 1) GC in time domain cannot correctly determine how strongly one time series influences the other when there is directional causality between two time series, and 2) spectral GC and other Granger-like causality measures have inherent shortcomings and/or limitations because of the use of the transfer function (or its inverse matrix) and partial information of the linear regression model. On the other hand, we propose two novel causality measures (in time and frequency domains) for the linear regression model, called new causality and new spectral causality, respectively, which are more reasonable and understandable than GC or Granger-like measures. Especially, from one simple example, we point out that, in time domain, both new causality and GC adopt the concept of proportion, but they are defined on two different equations where one equation (for GC) is only part of the other (for new causality), thus the new causality is a natural extension of GC and has a sound conceptual/theoretical basis, and GC is not the desired causal influence at all. By several examples, we confirm that new causality measures have distinct advantages over GC or Granger-like measures. Finally, we conduct event-related potential causality analysis for a subject with intracranial depth electrodes undergoing evaluation for epilepsy surgery, and show that, in the frequency domain, all measures reveal significant directional event-related causality, but the result from new spectral causality is consistent with event-related time-frequency power spectrum activity. The spectral GC as well as other Granger-like measures are shown to generate misleading results. The proposed new causality measures may have wide potential applications in economics and neuroscience.

Testing Frequency-Domain Causality in Multivariate Time Series

We introduce a new hypothesis-testing framework, based on surrogate data generation, to assess in the frequency domain, the concept of causality among multivariate (MV) time series. The approach extends the traditional Fourier transform (FT) method for generating surrogate data in a MV process and adapts it to the specific issue of causality. It generates causal FT (CFT) surrogates with FT modulus taken from the original series, and FT phase taken from a set of series with causal interactions set to zero over the direction of interest and preserved over all other directions. Two different zero-setting procedures, acting on the parameters of a MV autoregressive (MVAR) model fitted on the original series, were used to test the null hypotheses of absence of direct causal influence (CFTd surrogates) and of full (direct and indirect) causal influence (CFTf surrogates), respectively. CFTf and CFTd surrogates were utilized in combination with the directed coherence (DC) and the partial DC (PDC) spectral causality estimators, respectively. Simulations reproducing different causality patterns in linear MVAR processes demonstrated the better accuracy of CFTf and CFTd surrogates with respect to traditional FT surrogates. Application on real MV biological data measured from healthy humans, i.e., heart period, arterial pressure, and respiration variability, as well as multichannel EEG signals, showed that CFT surrogates disclose causal patterns in accordance with expected cardiorespiratory and neurophysiological mechanisms.

Assessing Frequency Domain Causality in Cardiovascular Time Series with Instantaneous Interactions

The partial directed coherence (PDC) is commonly used to assess in the frequency domain the existence of causal relations between two time series measured in conjunction with a set of other time series. Although the multivariate autoregressive (MVAR) model traditionally used for PDC computation accounts only for lagged effects, instantaneous effects cannot be neglected in the analysis of cardiovascular time series. We propose the utilization of an extended MVAR model for PDC computation, in order to improve the evaluation of frequency domain causality in the presence of zero-lag correlations among multivariate time series. A procedure for the identification of a MVAR model combining instantaneous and lagged effects is introduced. The coefficients of the extended model are used to estimate an extended PDC (EPDC). EPDC is compared to the traditional PDC on a simulated MVAR process and on real cardiovascular variability series. Simulation results evidence that the presence of zero-lag correlations may produce misleading PDC profiles, while the correct causality patterns can be recovered using EPDC. Application on real data leads to spectral causality estimates which are better interpretable in terms of the known cardiovascular physiology using EPDC than PDC. This study emphasizes the necessity of including instantaneous effects in the MVAR model used for the computation of PDC in the presence of significant zero-lag correlations in multivariate time series.

Real business cycles: is neglecting demand shocks justified?

Real business cycle models generally neglect demand shocks. Technological productivity shocks are the primary source of economic fluctuations. The multisectoral consequences of this assumption are described in the well-known model of Long and Plosser (1983). The presented paper shows that according to their view consumer goods sectors must be found in lagging positions. However, generalizing the strong assumption of pure supply driven dynamics by some demand-determined influences leads to ambiguous theoretical results such that only empirical evidence can answer the question whether sectoral lead-lag relationships are in accordance with real business cycle theory. Using cross spectral analysis and causality tests leads to a rejection of the Long and Plosser view of intersectoral comovements. On the contrary, the empirical results suggest that the backward propagation mechanism of demand shocks dominates the forward propagation of supply disturbances.